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Risk Analysis Real Options and Capital Budgeting Lecture 9, 10 Fall 2009

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Risk Analysis Real Options and Capital Budgeting Lecture 9, 10 Fall 2009

Corporate Finance

FINA 4330

Ronald F. Singer

- Sensitivity Analysis
- Break Even Analysis
- Monte Carlo Simulation
- Real Options and Decision Trees

- At any one time the firm has a number of projects that are possible.
- Typically, a number of projects are recommended by division heads
- The problem: Which of the proposed projects should be ultimately taken?
- Critical to this decision is what can go wrong:
- i.e. Uncertainty

- Sensitivity Analysis – What happens if certain variables are forecasted incorrectly?
- Scenario Analysis – What happens if a logical set of variables are forecasted incorrectly?
- Simulation Analysis – Alternative results when a large number of different scenarios are proposed.
- Break Even Analysis – What is the minimum level of sales (prices, costs) which still allows the project a non-negative NPV

- Define Costs as a function of output
- Define Revenue as a function of output
- Define expected (initial) variables
- Estimate worse and best case variables
- Get NPV’s for expected and also for worst case and best case situations
- Purpose: Determines where you might want to concentrate your efforts to assure correct forecasts

- The Company is thinking of introducing a new version of widgets designed for the under 30 crowd. To do this requires an initial investment of $150,000 and, at a production level of 10,000 units, it is expected to payoff $20,000 per year for 10 years. At the end of the ten years IWC will be able to sell the fixed assets and equipment for $100,000. If the real Cost of Capital is 4%, is this a good investment? All numbers are in real terms
- The NPV is: ???

- Initial Investment = $150,000
- Output (Q) = 10,000
- Life = 10 years
- Discount Rate = 4%
- Terminal Value = $100,000

The Model

- Cost = Fixed Cost + Unit cost X Quantity
= $10,000 + $6Q

- Revenues = Price X Quantity = $9Q
- Notice at output of 10,000: Cost = $70,000
Revenue = $90,000

Annual Payoff (Net Revenue) $20,000

Our original Scenario

- Pessimistic Optimistic
- Initial Investment 155 140
- Sales price 8 10
- Fixed cost 12 8
- Unit Variable Cost 7 5
- Output 9 13
- Life 8 12
- Discount Rate 5% 3%
- Scrap Value 95 120
- See excel file: International Widget Company

- What does Sensitivity analysis Tell You?

- We have assumed that inflation, over the period will be zero. What if we assume that the inflation rate is 1% per year
- We have to forecast the impact on the variables in the model. Suppose we forecast that REAL variable costs, and revenues will remain the same. But that the REAL fixed cost will decline by $1,000.
- Then the impact of inflation on annual cash flow will be:
- Real CF will increase to $21,000

- Also we forecast that this will impact on the real terminal value of the assets will decline to $90,000, from the original $100,000.
.

- What is the new NPV?

- Breakeven is that level of output for which the investment “breaks even”
- What is meant by “breaks even”
- Where NPV = 0

- What is that in terms of output?

- Notice that the (real) margin is $2 per unit, and Cash Flow is the margin times the units sold,
- That is CF = (Sale price-Unit cost)*Units sold
= (Margin)*Units sold

= (2.00)* 10,000 = $20,000

- What is the minimum units you have to sell to “break even” in PV terms? That is: what is the sales level which will give you a zero NPV.

- That is CF = (Sale price-Unit cost)*Units sold
- The Cash Flow’s PV must equal $150,000
- How do you do this? Find the Payments that have a PV of $150,000
- So Breakeven is:
- So quantity must be ???

Modeling Process

- Step 1: Modeling the Project
- Step 2: Specifying Probabilities
- Step 3: Simulate the Cash Flows

- Decision Trees - Diagram of sequential decisions and possible outcomes.
- Embedded in a typical project are options which are not adequately dealt with by the standard DCF Analysis.
- These Options are typically contingent on observing new information as time goes by.
- For example, options:
- To Expand,
- Contract
- Cease Operations or abandon

- Decision trees help companies determine their Options by showing the various choices and outcomes.
- The ability to create an Option thus has value that should be included in the PV of a project

- Search for projects with a positive NPV.
- Typically this entails generating a stream of Expected Cash Flows and appropriately discounting.
- However, this could miss some of the strategic value associated with an investment opportunity.
- That is, the ability to react to new information after the project has begun.

- Views the Firm in a dynamic setting
- Firm is searching for and capitalizing on its comparative advantage
- Emphasis on the ability of the firm to react to complex situations
- Emphasis on the firm’s reaction to change and capitalizing on changing environment

- Typically the cash flow from an investment is determined initially with no concept of dynamic reactions.
- The use of Real Options allows us to integrate the two concepts into project analysis.

- Thinking of expanding into China: the plant will cost $3 million to build and the marketing department tells you that the market will generate the equivalent of about $500,000 per year forever if successful, but may produce as little as $50,000 per year if unsuccessful. the probability of success is 50%. At a 10% discount rate, what is the NPV of the project.
- Accept or Reject this project?

- If you develop a pilot project it will only cost $200,000 and if successful, then the pilot project will generate $80,000 if unsuccessful it will only generate $30,000, each outcome equally likely . In either case, the pilot project will not be able to be continued thereafter.
- Note that this is a losing project by itself, but it does allow you to get valuable information about the full scale production

- Marketing people tell you that if the pilot project is successful, then there is a 90% chance of the full scale project being successful and generating $500,000 and year, but if the pilot project is unsuccessful then the full scale project will only generate the $500,000 with a probability of 25%.
- Should we (1) undertake the Pilot Project, (2) go immediately into production full scale, or (3) do neither?

5,000,000

90%

-3,000,000

10%

80,000

500,000

50%

NPV = 0 (stop)

5,000,000

25%

-200,000

-3,000,000

50%

75%

500,000

30,000

NPV = 0 (stop)

5,000,000

90%

-3,000,000

80,000

10%

Continue

500,000

50%

STOP

NPV = 0

5,000,000

25%

-200,000

-3,000,000

50%

75%

500,000

Continue

30,000

STOP

NPV = 0

5,000,000

90%

-3,000,000

80,000

10%

500,000

Continue

50%

STOP

NPV = 0

5,000,000

25%

-200,000

-3,000,000

50%

75%

500,000

Continue

30,000

NPV = 0

STOP

NPV(1) = $1,550,000

80,000

Continue

50%

-200,000

50%

30,000

NPV = 0

STOP

80,000 + 1,550,000 = $1,630,000

50%

NPV OF Total is: $740.909 + 13,636 -200,000 = 554,545

-200,000

50%

30,000